Nigeria has sought to crush the group with military force but faces criticism from human rights activists for alleged extra-judicial killings.

The military said some battalions had received training in the US. "The army is in the process of setting up a division that is effectively looking at warfare tactics," a spokesman said. "Various battalions were in the United States earlier this year for training to that end."

It is though these include specialist units such as bomb disposal.

US officials confirmed it has a longstanding deal with Nigeria with soldiers travelling to America for training. It could not comment on whether the exercises was aimed at combating Boko Haram.

The US embassy in Abuja said: "We have had a mil-mil relationship with the Nigerians for decades, principally supporting their peacekeeping efforts in Africa (Liberia, Sierra Leone, Darfur) and around the globe. In recent years, and at their request, we have also worked with them on their nascent counter-force. We do not know if any of these elements have been deployed in the north."

Boko Haram has overtaken militants in the oil-rich Niger delta as the country's main security problem. Loosely modelled on the Taliban in Afghanistan, it became active in 2003 and is focused mainly in the impoverished northern states of Yobe, Kano, Bauchi and Borno.

The group's official name is Jama'atu Ahlis Sunna Lidda'awati wal-Jihad, which in Arabic means, "People Committed to the Propagation of the Prophet's Teachings and Jihad". But Hausa-speaking residents in the city of Maiduguri, the group's spiritual home, call it Boko Haram, usually translated as "Western education is forbidden/ sinful".

Anger at years of poor local governance, corruption and endemic poverty found a voice at the mosques. The group considers all who do not follow its strict ideology as infidels, whether they are Christian or Muslim. It demands sharia, Islamic law, across Nigeria.

The sect's modus operandi includes using motorbikes for drive-by shootings. In December 2010, the sect said it was behind bombings in central Nigeria and attacks on churches in the north-east that led to the deaths of at least 86 people. At least 361 people have been killed this year, according to the Associated Press.

In June, a car bomb tore through a car park outside the police headquarters in the capital, Abuja, killing at least two people, demonstrating Boko Haram could attack the heart of Nigerian society. In August, Nigeria's first suicide bomber struck the UN building in Abuja, killing 23 people.

Last Friday, a series of suicide bombings and shootings left more than 100 people dead in Damaturu, the capital of rural Yobe state. They were followed by the killing of a police inspector on Sunday in Maiduguri. Men stopped the officer's car at gunpoint as he neared a mosque to pray, ordered his family away, then shot him dead.

President Goodluck Jonathan, a Christian, appeared on national television wearing a prayer cap and the traditional robes of the country's Muslim north to mark the Eid al-Adha holiday. "We're all expected to live in peace, but as a nation, we have our own challenges," he said. "During this holy period, we still have incidents happening here and there."

But the mood in Maiduguri remains tense. Ali Sambo, co-ordinator of the National Emergency Management Agency, said: "It's a festive period and normally people would be out amusing themselves … But everyone is fearful… There are roadblocks and a curfew. "The issue here is that Boko Haram are members of the community. There's nothing to single them out; they are free to move around like any other citizen. How the police will deal with that is the big question."

Some claim the military's iron fist approach is counter-productive. Activist Shehu Sani, president of Civil Rights Congress of Nigeria , said he tried to broker a ceasefire between Boko Haram and the government two months ago, but the talks collapsed when one of the hosts was killed. "Boko Haram blamed the security forces," he said.

"The government is insisting on using the military to end the group. But groups always counter state violence with their own violence. We are actually in a state of armed Islamic insurgency in the north-east of Nigeria. For now it is most likely Boko Haram will expand their operations to other parts of Nigeria to make a point and prove they are really on the ground."